Ou-Iang积分不等式的推广

本文推广了Ou-Iang在文[1]中给出的一类积分不等式。     

一类迭代微分方程的解析解

给出一类 n阶迭代泛函微分方程 x( n) =a∏li=1(x[mi] (qiz) ) ki的形如 x(z) =λzμ的解的存在性     

大学物理实验在微信公众号线上学习模式的探究

在互联网背景下,微信公众号具有使用普遍性、图文形式多样性、传递的快捷性等特点.我们通过问卷调查掌握学生在大学物理实验学习中的难点,有重点地将大学物理实验课程学习资源推送到微信公众号中,创建物理实验学习的线上模式,为大学物理实验学习搭建一种新的学习平台.     

一类二阶迭代泛函微分方程的解析解

本文研究了一类二阶迭代泛函微分方程ｘ″（ｚ）＝ｍｊ＝０ｐｊｘｊ（ｚ），ｚ∈Ｃ．其中ｍ为正整数，ｘｊ（ｚ）表示未知函数ｘ（ｚ）的ｊ次迭代，给出了这类方程满足初始条件解析解的几个存在性定理．     

关于某些函数积分方程的解析解

在本文中,我们给出了函数积分方程(1)—(3)解析解的存在唯一性和渐近性定理。在文献[1]和[2]中分别给出了下面三类函数积分方程     

Design and fabrication of a micro thermal actuator for cellular grasping

The development of a novel polymer-based micro robotic gripper that can be actuated in a fluidic medium is presented in this paper. Our current work is to explore new materials and designs for thermal actuators to achieve micromanipulation of live biological cells. We used parylene C to encapsulate a metal heater, resulting in effectively a tri-layered thermal actuator. Parylene C is a bio-compatible dielectric polymer that can serve as a barrier to various gases and chemicals. Therefore, it is suitable to serve as a thermal/electrical/chemical isolation material for protecting the metal heater from exposing to an aqueous environment. We have demonstrated parylene actuators(2 mm×100/μm×0.5μm) to operate in an aqueous environment using 10 to 80 mW input power. The temperature of these actuators at full deflection was estimated to be～ 60℃, which is much lower than the typical requirement of > 100℃ to actuate other conventional MEMS actuators. Danio rerio follicles in fluidic medium were captured successfully using these actuators. Moreover, these actuators were found to be responsive to moderate rise in environmental temperature, and hence, we could vary the fluidic medium temperature to actuate trimorphs on a chip without any input of electrical energy, i.e., raising the fluidic temperature from 23℃ to 60℃ could actuate the trimorphs to grasp follicles of～1mm size in diameter. At 60℃, the embryos inside the follicles were observed to be alive, i.e., they were still moving in the biological fluid isolated by the follicle membrane. The smallest follicles grasped were～500μm in diameter using 800μm×130μm×0.6μm actuators. The fabrication process, modeling, and optimization of the trimorph actuators are presented. Based on the successful operation of these polymer-based actuators, we are currently developing multifinger thermal microgrippers for cellular grasping and manipulation, which can potentially be hybridly integrated with circuits for computer control.     

关于中值定理“中间点”的渐近性

<正> 中值定理在数学分析中的重要意义是众所周知的.无论微分中值定理(包括泰勒定理)或积分中值定理,实际上都是适合特定等式的某区间内的“中间点”的存在定理.中值定理虽能肯定“中间点”的存在性,但却没有给出确定“中间点”位置的方法,诚然,这种不确定性并不影响中值定理有着多方面的应用.     

两类Jabotinsky微分方程的解析解

在本文中，我们利用优级水清给出Ｊａｂｏｔｉｕｓｋｙ方程（Ｊ２）和（Ｊ３）解析解存在性的一些充分条件。     

利用函数方程证明二项展开定理

众所周知,函数f(x)=(1+x)~α的泰勒(Taylor)级数具有如下的形式 级数(1)常称为牛顿(Newton)二次式级数。在此,我们不妨假定α是异于非负整数的实数。事实上,当α取正整数时,级数(1)就变成了人们熟知的有穷的二项展开式了。     

关于推广的积分中值定理的一个注记

本文在一般情况下讨论了推广的积分中值定理“中间点”的渐近性 ,从而给出了具有普遍意义的结果 .